Thread: Maths assignment - compound interest or geometric progression

Question 4
Capital invested with interest, may be compounded at any time interval, (quarterly, daily or continuously) for any set time period. The formula used for discrete intervals of time is given by: FV = PV (1+r)^n
(FV is future value, PV is present value, r is interest rate for the time interval, n is number of time intervals)
a) Find the return on $100 investment compounded daily at 6%p.a. for 10 years

a) FV =?
PV = $100
r= 0.06/365.25 = 0.0001642710472
n= 3652.5

PV (1+r)^n
= $100 (1+0.0001642710472)^3652.5
= $182.20
Is that right? Or am i meant to do it like a geometric progression? If so, what is the geometric progression formula? I learnt it today but i left my workbook at school.

Yep, what you've done is correct.

I think the geometric progression you're talking about is just the long way around, eg recalculating with a different principal after each interest payment - which would mean 3653 calculations for daily compounding! I'd say you picked the right method

Who actually uses 365.25 in practice? If you REALLY want to account for Leap Year across millenia, you shoud use 365.2475.

Unless you are specifically required to use 365.25, I would avoid it. Anyway, over a 10-year period, you will hit either two (avg. 365.20 days) or three (avg. 365.30 days) leap years. 365.25 is a little arbitrary.

Originally Posted by bubbles73

Question 4
Capital invested with interest, may be compounded at any time interval, (quarterly, daily or continuously) for any set time period. The formula used for discrete intervals of time is given by: FV = PV (1+r)^n
(FV is future value, PV is present value, r is interest rate for the time interval, n is number of time intervals)
a) Find the return on $100 investment compounded daily at 6%p.a. for 10 years

a) FV =?
PV = $100
r= 0.06/365.25 = 0.0001642710472
n= 3652.5

PV (1+r)^n
= $100 (1+0.0001642710472)^3652.5
= $182.20
Is that right? Or am i meant to do it like a geometric progression? If so, what is the geometric progression formula? I learnt it today but i left my workbook at school.

This question does not belong in the probability and statistics forum.